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Standard Deviation, SM-Bank 003

In a small business, the seven employees earn the following wages per week:

\(\$300, \ \$490, \ \$520, \ \$590, \ \$660, \ \$680, \ \$970\)

  1.  Calculate the standard deviation for this set of data, giving your answer to one decimal place.  (1 mark)

  2.  Each employee receives a $20 pay increase.

     

     Explain the effect that this increase will this have on the standard deviation?  (2 marks)

Show Answers Only

i.    \(191.0\)

ii.    \(\text{All values increase by \$20, but so too does the mean.} \)

\(\text{Therefore the spread about the new mean will not change} \)

\(\text{and therefore the standard deviation will remain the same.} \)

Show Worked Solution

i.    \(\text{By calculator (in Statistics mode:}\)

\(\text{Std Dev}\ = 191.044...  =191.0\ \text{(1 d.p.)} \)


ii.    \(\text{All values increase by \$20, but so too does the mean.} \)

\(\text{Therefore the spread about the new mean will not change} \)

\(\text{and therefore the standard deviation will remain the same.} \)